Some recent advancements of the nuclear many-body theory and selected results on nuclear giant and pygmy resonances are presented. The theory is compactly reviewed, with a special focus on the emergent scale of the quasiparticle-vibration coupling (qPVC), which carries the order parameter associated with the qPVC vertex, and an efficient treatment of the nuclear many-body problem organized around the qPVC hierarchy. Self-consistent numerical solutions of the relativistic Bethe-Salpeter-Dyson equation for the nuclear response function in medium-heavy nuclei are discussed. The presented update on the pygmy dipole resonance focuses on establishing the formation of its two-component structure as a result of the fragmentation of the low-energy dipole mode due to the qPVC and its mixing with the similarly fragmented giant dipole resonance. The centroid of the isoscalar giant monopole resonance is also linked to qPVC effects, particularly to its sensitivity to the coupling of the collective breathing mode to the lowest quadrupole vibrations, which is enhanced by quadrupole collectivity. The resolution of the long-standing "fluffiness" puzzle regarding the compressibility of open-shell tin isotopes is summarized. The recently developed thermal variant of the superfluid response theory is briefly introduced and continuously linked to the description of the isoscalar monopole response at finite temperature with the prospect of refining the temperature-dependent nuclear equation of state.
Some recent advancements of the nuclear many-body theory and selected results on nuclear giant and pygmy resonances are presented. The theory is compactly reviewed, with a special focus on the emergent scale of the quasiparticle-vibration coupling (qPVC), which carries the order parameter associated with the qPVC vertex, and an efficient treatment of the nuclear many-body problem organized around the qPVC hierarchy. Self-consistent numerical solutions of the relativistic Bethe-Salpeter-Dyson equation for the nuclear response function in medium-heavy nuclei are discussed. The presented update on the pygmy dipole resonance focuses on establishing the formation of its two-component structure as a result of the fragmentation of the low-energy dipole mode due to the qPVC and its mixing with the similarly fragmented giant dipole resonance. The centroid of the isoscalar giant monopole resonance is also linked to qPVC effects, particularly to its sensitivity to the coupling of the collective breathing mode to the lowest quadrupole vibrations, which is enhanced by quadrupole collectivity. The resolution of the long-standing "fluffiness" puzzle regarding the compressibility of open-shell tin isotopes is summarized. The recently developed thermal variant of the superfluid response theory is briefly introduced and continuously linked to the description of the isoscalar monopole response at finite temperature with the prospect of refining the temperature-dependent nuclear equation of state.
Some recent advancements of the nuclear many-body theory and selected results on nuclear giant and pygmy resonances are presented. The theory is compactly reviewed, with a special focus on the emergent scale of the quasiparticle-vibration coupling (qPVC), which carries the order parameter associated with the qPVC vertex, and an efficient treatment of the nuclear many-body problem organized around the qPVC hierarchy. Self-consistent numerical solutions of the relativistic Bethe-Salpeter-Dyson equation for the nuclear response function in medium-heavy nuclei are discussed. The presented update on the pygmy dipole resonance focuses on establishing the formation of its two-component structure as a result of the fragmentation of the low-energy dipole mode due to the qPVC and its mixing with the similarly fragmented giant dipole resonance. The centroid of the isoscalar giant monopole resonance is also linked to qPVC effects, particularly to its sensitivity to the coupling of the collective breathing mode to the lowest quadrupole vibrations, which is enhanced by quadrupole collectivity. The resolution of the long-standing “fluffiness” puzzle regarding the compressibility of open-shell tin isotopes is summarized. The recently developed thermal variant of the superfluid response theory is briefly introduced and continuously linked to the description of the isoscalar monopole response at finite temperature with the prospect of refining the temperature-dependent nuclear equation of state.
Nonperturbative aspects of the quantum many-body problem are revisited, discussed and advanced in the equation of motion framework. We compare the approach to the two-fermion response function truncated on the two-body level by the cluster expansion of the dynamical interaction kernel to the approach known as time blocking approximation. Such a comparison leads to an extended many-body theory with nonperturbative treatment of high-order configurations. The present implementation of the advanced theory introduces a new class of solutions for the response functions, which include explicitly beyond-mean-field correlations between up to six fermions. The novel approach, which includes configurations with two quasiparticles coupled to two phonons ($2\mathrm{q}\ensuremath{\bigotimes}2\mathrm{phonon}$), is discussed in detail for the particle-hole nuclear response and applied to medium-mass nuclei. The proposed developments are implemented numerically on the basis of the relativistic effective meson-nucleon Lagrangian and compared to the models confined by two-fermion and four-fermion configurations, which are considered as state-of-the-art for the response theory in nuclear structure calculations. The results obtained for the dipole response of 42,48Ca and 68Ni nuclei in comparison to available experimental data show that the higher configurations are necessary for a successful description of both gross and fine details of the spectra in both high-energy and low-energy sectors.
This thesis is a collection of theoretical investigations into different aspects of the broad subject of quantum many-body theory. The results are grouped into three main parts, which in turn are divided into separate self-contained sections. Some of the work is presented in the form of published papers and papers that have been submitted for publication. The first section of Part A introduces some of the concepts involved in many-body problems, by developing methods to evaluate expectation values of the form . In the rest of Part A I consider collective excitations of finite quantum systems. The calculations are confined to nuclei because the results can then be compared with the extensive investigations that have been made into collective nuclear modes. In Section AII, wavefunctions are proposed for rotational excitations of even-even nuclei. Both isoscalar and isovector nuclear modes are discussed. In particular, the l2,m> isoscalar states are investigated for both spherical and deformed even-even nuclei, and the simplest isovector wavefunction is shown to give a good description of the giant dipole resonance. In section AIII wavefunctions are proposed for compressional vibrational states of spherical nuclei. Section AIV discusses sum rules for nuclear transitions of a given electric multipolarity. It is found that the 2+ and 1- states investigated in section AII and all but one of the vibrational states discussed in AIII each exhaust a large part of the appropriate sum rule. In Part B I consider the problem of how to describe flow in quantum fluids. In particular, we want to be able to identify the physical motion represented by any given many-body wavefunction. Section BI derives a guantum mechanical velocity field for a many-body system, paying special attention to the need for a quantum continuity equation. It is found that when the wavefunction has the usual time dependence e-iwt , that the quantum velocity formula averages over all oscillatory motion, so that much of the physical nature of the flow field is lost. In section BII a particular wavefunction is proposed to represent the quantum excitation corresponding to any given potential flow field. The results obtained by considering specific examples are very encouraging. In Part C I investigate the properties of surfaces. Section CI presents a theoretical description of the tension, energy and thickness of a classical liquid-vapour interface. In section CII the classical results are extended to describe the surface of a quantum system, namely superfluid helium four. Problems occur for the quantum system if the correlations arising from the zero-point-motion of the phonon modes are included in the ground state wavefunction. Finally, in section CIII discuss generalized virial theorems that give the change in the free energy of a system undergoing an infinitesimal deformation. For example, a particular deformation gives the expression used in CII, for the surface tension of a plane quantum surface.
This thesis is a collection of theoretical investigations into different aspects of the broad subject of quantum many-body theory. The results are grouped into three main parts, which in turn are divided into separate self-contained sections. Some of the work is presented in the form of published papers and papers that have been submitted for publication. The first section of Part A introduces some of the concepts involved in many-body problems, by developing methods to evaluate expectation values of the form . In the rest of Part A I consider collective excitations of finite quantum systems. The calculations are confined to nuclei because the results can then be compared with the extensive investigations that have been made into collective nuclear modes. In Section AII, wavefunctions are proposed for rotational excitations of even-even nuclei. Both isoscalar and isovector nuclear modes are discussed. In particular, the l2,m> isoscalar states are investigated for both spherical and deformed even-even nuclei, and the simplest isovector wavefunction is shown to give a good description of the giant dipole resonance. In section AIII wavefunctions are proposed for compressional vibrational states of spherical nuclei. Section AIV discusses sum rules for nuclear transitions of a given electric multipolarity. It is found that the 2+ and 1- states investigated in section AII and all but one of the vibrational states discussed in AIII each exhaust a large part of the appropriate sum rule. In Part B I consider the problem of how to describe flow in quantum fluids. In particular, we want to be able to identify the physical motion represented by any given many-body wavefunction. Section BI derives a guantum mechanical velocity field for a many-body system, paying special attention to the need for a quantum continuity equation. It is found that when the wavefunction has the usual time dependence e-iwt , that the quantum velocity formula averages over all oscillatory motion, so that much of the physical nature of the flow field is lost. In section BII a particular wavefunction is proposed to represent the quantum excitation corresponding to any given potential flow field. The results obtained by considering specific examples are very encouraging. In Part C I investigate the properties of surfaces. Section CI presents a theoretical description of the tension, energy and thickness of a classical liquid-vapour interface. In section CII the classical results are extended to describe the surface of a quantum system, namely superfluid helium four. Problems occur for the quantum system if the correlations arising from the zero-point-motion of the phonon modes are included in the ground state wavefunction. Finally, in section CIII discuss generalized virial theorems that give the change in the free energy of a system undergoing an infinitesimal deformation. For example, a particular deformation gives the expression used in CII, for the surface tension of a plane quantum surface.
A consistent finite-temperature microscopic theory for the response of strongly coupled superfluid fermionic systems is formulated. We start from the general many-body Hamiltonian with the vacuum (bare) two-fermion interaction and derive the equation of motion (EOM) for the thermally averaged two-time two-fermion correlation function, which determines the spectrum of the system under study. The superfluidity is introduced via the Bogoliubov transformation of the fermionic field operators, and the entire formalism is carried out in the basis of Bogoliubov's quasiparticles, keeping the complete 4x4 block matrix structure of the two-fermion EOM. Fully correlated static and dynamical interaction kernels of the resulting EOM are discussed. A special focus is then placed on the latter kernel, which is advanced to a factorized form, enabling a minimal truncation of the many-body problem while keeping important effects of emergent collectivity and mapping to the quasiparticle-vibration coupling (qPVC). As in the zero-temperature and non-superfluid cases, the qPVC can be associated with a new order parameter, qPVC vertex. In the thermal superfluid theory, the latter vertex, as well as the components of the dynamical kernel, acquire an extended form including thermally unblocked transition amplitudes.
This thesis is a collection of theoretical investigations into different aspects of the broad subject of quantum many-body theory. The results are grouped into three main parts, which in turn are divided into separate self-contained sections. Some of the work is presented in the form of published papers and papers that have been submitted for publication. The first section of Part A introduces some of the concepts involved in many-body problems, by developing methods to evaluate expectation values of the form . In the rest of Part A I consider collective excitations of finite quantum systems. The calculations are confined to nuclei because the results can then be compared with the extensive investigations that have been made into collective nuclear modes. In Section AII, wavefunctions are proposed for rotational excitations of even-even nuclei. Both isoscalar and isovector nuclear modes are discussed. In particular, the l2,m> isoscalar states are investigated for both spherical and deformed even-even nuclei, and the simplest isovector wavefunction is shown to give a good description of the giant dipole resonance. In section AIII wavefunctions are proposed for compressional vibrational states of spherical nuclei. Section AIV discusses sum rules for nuclear transitions of a given electric multipolarity. It is found that the 2+ and 1- states investigated in section AII and all but one of the vibrational states discussed in AIII each exhaust a large part of the appropriate sum rule. In Part B I consider the problem of how to describe flow in quantum fluids. In particular, we want to be able to identify the physical motion represented by any given many-body wavefunction. Section BI derives a guantum mechanical velocity field for a many-body system, paying special attention to the need for a quantum continuity equation. It is found that when the wavefunction has the usual time dependence e-iwt , that the quantum velocity formula averages over all oscillatory motion, so that much of the physical nature of the flow field is lost. In section BII a particular wavefunction is proposed to represent the quantum excitation corresponding to any given potential flow field. The results obtained by considering specific examples are very encouraging. In Part C I investigate the properties of surfaces. Section CI presents a theoretical description of the tension, energy and thickness of a classical liquid-vapour interface. In section CII the classical results are extended to describe the surface of a quantum system, namely superfluid helium four. Problems occur for the quantum system if the correlations arising from the zero-point-motion of the phonon modes are included in the ground state wavefunction. Finally, in section CIII discuss generalized virial theorems that give the change in the free energy of a system undergoing an infinitesimal deformation. For example, a particular deformation gives the expression used in CII, for the surface tension of a plane quantum surface.